Aggressive motions from agile flights or traversing irregular terrain induce motion distortion in LiDAR scans that can degrade state estimation and mapping. Some methods exist to mitigate this effect, but they are still too simplistic or computationally costly for resource-constrained mobile robots. To this end, this paper presents Direct LiDAR-Inertial Odometry (DLIO), a lightweight LiDAR-inertial odometry algorithm with a new coarse-to-fine approach in constructing continuous-time trajectories for precise motion correction. The key to our method lies in the construction of a set of analytical equations which are parameterized solely by time, enabling fast and parallelizable point-wise deskewing. This method is feasible only because of the strong convergence properties in our novel nonlinear geometric observer, which provides provably correct state estimates for initializing the sensitive IMU integration step. Moreover, by simultaneously performing motion correction and prior generation, and by directly registering each scan to the map and bypassing scan-to-scan, DLIO’s condensed architecture is nearly 20% more computationally efficient than the current state-of-the-art with a 12% increase in accuracy. We demonstrate DLIO’s superior localization accuracy, map quality, and lower computational overhead as compared to four state-of-the-art algorithms through extensive tests using multiple public benchmark and self-collected datasets.